Jambmaths question:
The binary operation * is defined on the set of real numbers is defined by $m*n=\frac{mn}{2}$for all$m,n\in \mathbb{R}$. If the identity element is 2. Find the inverse of –5 .
Option A:
$-\tfrac{4}{5}$
Option B:
$-\tfrac{2}{5}$
Option C:
4
Option D:
5
Jamb Maths Solution:
$\begin{align} & m*n=\frac{mn}{2} \\ & \text{Let }{{m}^{-1}}\text{ be inverse of }m \\ & \therefore m*{{m}^{-1}}=e\text{ }\!\!\{\!\!\text{ }e\text{ is the identity element }\!\!\}\!\!\text{ } \\ & 5*{{m}^{-1}}=2 \\ & 5*{{m}^{-1}}=\frac{5\times {{m}^{-1}}}{2}=2 \\ & 5{{m}^{-1}}=4 \\ & {{m}^{-1}}=\tfrac{4}{5} \\\end{align}$
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